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©2012 Civil-Comp Ltd |
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E. Myšáková, M. Lepš and A. Kucerová
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic
Keywords: design of experiments, latin hypercube sampling, constrained design spaces, non-regular design spaces, space-filling, Delaunay triangulation.
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reference
Space-filling design strategies known as design of experiments (DoE) constitute
an essential part of any experimentation. This paper concerns one particular
domain of constrained design spaces. The most frequent example is the case of
a mixture experiment, where individual inputs form a unity volume or unity weight
[1]. This single condition leads to the simplex space; further limits
on individual inputs then form a polytope, still convex but generally an irregular space.
Therefore, all traditional DoEs [1] that are constructed for hypercube
spaces cannot be applied here. Although the problem of mixture experiments has been
known for decades, the progress of the methods for DoEs does not follow current developments.
In this paper a different approach based on Delaunay triangulation (DT) of
an admissible domain and a utilization of the properties of the Distmesh tool
(DM) [2] is presented. In the authors' method the domain described
by corner vertices is triangulated using DT and the desired number of random points is
generated inside. Then the DM tool is applied. The Distmesh tool is a heuristic
smoothing algorithm for generating uniform meshes that is based on a simple dynamic
system of an expanding pin-jointed structure. Those trusses that are too short
cause repulsive forces that move apart nodes that are too close creating uniformly
spaced points.
The results are compared with seven constrained examples in two dimensions and
one three dimensional example presented in [3], namely
a placing of design points in a triangle, parallelogram, pentagon, hexagon, heptagon,
octagon, irregular hexagon and prism. Although not designed directly for space-filling
optimization, our procedure is able to outperform the reference algorithm even from
the D-optimal point of view; however, only in two-dimensions as is shown in the paper.
- 1
- D.C. Montgomery, "Design and Analysis of Experiments", 5th Edition, Wiley, 2000.
- 2
- P.-O. Persson, G. Strang, "A simple mesh generator in MATLAB", SIAM Review, 46(2), 329-345, 2004.
- 3
- M. Hofwing, N. Strömberg, "D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method", Structural and Multidisciplinary Optimization, 42, 73-88, 2010.
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